Approximate Mean Value Analysis of a Database Grid Application Dale R. Thompson Computer Science and Computer Engineering University of Arkansas March 1, 2004

Contents Introduction Queueing Network System MVA algorithms Comparison of AMVA Proposed System Current Queueing Model CPU and Network Demand Maximum Throughput and Block Size Uniform Distribution Nonuniform Distribution Uniform : number of Clients Proposed change to application Segregation of batch and interactive classes Conclusion Future Work March 1, 2004

Introduction A database grid application is modeled using an approximate mean value analysis algorithm. The system is represented by a queueing network. The analysis of a queueing network is important for predicting the performance of a system. Several algorithms will be explained and compared. Database grid application is introduced and the performance objectives are defined and analyzed by using an approximate MVA algorithm called the Bard-Schweitzer algorithm or the proportional estimate (PE) algorithm. Several models will be modeled. For example, uniform, non-uniform, etc. A system in which the batch and interactive requests are segregated is modeled. Conclusions of analysis. March 1, 2004

Queueing Network System server client queue [Single class queueing server] client2 [Multiple class queueing server] client3 client1 March 1, 2004

when class c is a batch processing, MVA algorithms when class c is a batch processing, Zc=0 Mean Value Analysis calculates throughput (Xc), response time (Rc), and queue length (Qd,c)of each class. It can be classified with the number of client – open or closed. It also can be classified with how to get the values Exactly or Approximately. Single class or multiple classes? When Queueing Server, When Delay Server, March 1, 2004

Classification of MVA algorithms March 1, 2004

Comparison of AMVA algorithms Rank of Accuracy Space Complexity Time Complexity Exact MVA 1 O(KC∏Cc=1(Nc+1) Linearizer 2 O(KC2)/iteration O(KC3)/iteration PE 3 O(KC)/iteration LCP 4 Algorithms Rank of Accuracy Space Complexity Time Complexity No con. Congestion Exact MVA 1 O(KC∏Cc=1(Nc+1) FL 2 4 O(KC)/iteration QL 3 PE 1. Average errors in throughput and response time for three algorithm is less than 1%~2%. 2. QL is a little bit better than PE algorithm when congestion. So, they are not much different. 3. We decided use PE algorithm for analyzing our system. March 1, 2004

Proposed System Database Link Application Example Director grid services the particular client and receives the block of records and splits the records according to a key. Database grid is logically partitioned to serve different keys. March 1, 2004 Database Link Application Example High-level Overview of System

A high-level view of the grid Cont. A high-level view of the grid The Flow of Records March 1, 2004

Current Queueing Model March 1, 2004 Queueing Model

CPU and Network Demand Record size - 500bytes, Ethernet - 26bytes, IP - 20bytes, TCP - 20bytes. Total actual record size - 566bytes Service demand1 : computers in the clients, the director grid, and database grid. Service demand2 : network cards in the clients, the director grid, and database grid. March 1, 2004

Maximum Throughput and Block size Maximum attainable throughput : 79.5Mega record/hr The block size : Batch class : 1150 records Interactive class : 1 record. March 1, 2004

Uniforms Distributions Each record was equally likely to go to any of the computers in the database grid, Block size : varying Throughput : 20 directors(79.2 MR/hr), 15 directors(59.4 MR/hr), 10 directors(39.7 MR/hr) Delay time : 20 directors(0.0523 S/R), 15 directors(0.0783 S/R), 10 directors(0.0523 S/R) March 1, 2004

Non-uniform Distribution Non-uniform distribution of demands was created by assuming that 20 clients : 10,15,20 director computers : 70 database computers 80% of the requests from clients (16 clients) => 20% of the database grid (14 Computers). The remaining 20% of the requests (4 clients)=> the remaining 80% of the database grid (56 Computers) Throughput (Mrecords/hr) 10 directors 15 directors 20 directors Uniform 40 59 79 Non-uniform 71 Delay time (s/records) 0.1043 0.0783 0.0523 0.0581 1. If all clients distribute their requests uniformly across the database grid, the overall efficiency of the system improves. 2. To demonstrate this affect on the performance, a uniform distribution of demands was compared with a non-uniform distribution of demands both using a block size of 1150 March 1, 2004

Uniform : Number of Clients Uniform : 1150 records Varying number of Clients : 20, 40, 60 Throughput (Mrecords/hr) 20 clients 40 clients 60 clients 10 directors 40 20 13 15 directors 59 30 20 directors 79 26 Delay time (s/record) 0.1043 0.2084 0.3126 0.0783 0.1433 0.0523 0.1564 March 1, 2004

Proposed Change to application It assume that there are two times update (new geo. and old geo.) This proposed change was modeled by having 5% of the clients (1 client out of 20) require demand from two different database grid computers. Block size : 1150 records Throughput (Mrecords/hr) 10 directors 15 directors 20 directors Original Application 40 59 79 Proposed Application 39 57 77 % decrease 2.50 3.32 2.49 Delay time (s/record) 0.1043 0.0783 0.0523 0.1095 0.0809 0.0549 % increase 4.98 4.97 March 1, 2004

Segregation of batch and interactive classes This model is for the real system. 20 clients : 16 director computers : 70 database computers. There are 12 clients batch and 8 clients interactive record. Batch 12 clients => 12 directors Interactive 8 clients => 4 directors. Throughput (Mrecords/hr) Interactive 3.4 Batch 47.5 Total 50.9 Avg. Delay (s/record) 0.0002 0.0314 0.0316 This reduces the mean delay per record to better serve the interactive clients The database link application could use the 0.0002 s/record parameter as a design parameter March 1, 2004

Conclusions of Work First, the number of directors should be approximately equal to the number of clients to obtain the maximum throughput of the system. Second, the bottleneck device in this system is the network. The proposed application change that caused 5% of the records to require service from two database grid computers did not significantly decrease the performance of the system. Segregating the batch and interactive classes at the director level causes the response time of the interactive classes to decrease. The decreased response time comes at the price of lowering the overall throughput of the system. As discussed, the model can be used to determine the trade offs of decreased response time versus increased throughput. March 1, 2004

Future Work Traffic analysis of submitted records Simulation of alternate configurations Scheduling of grid computers Modeling/Simulation of different applications Grid-enable applications that run in different locations and organizations Others? March 1, 2004